To simplify \( 5^{10} \cdot 5^{5} \) using the Product Rule of Exponents, you add the exponents. The Product Rule states that \( a^m \cdot a^n = a^{m+n} \).
In this case:
\[ 5^{10} \cdot 5^{5} = 5^{10 + 5} = 5^{15} \]
Therefore, the simplified expression is:
5^15 (or 5 to the 15th power)